Optimal. Leaf size=24 \[ \sqrt{2} F\left (\sin ^{-1}\left (\frac{\sqrt{x+1}}{\sqrt{3}}\right )|-\frac{3}{2}\right ) \]
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Rubi [A] time = 0.0407108, antiderivative size = 24, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.042 \[ \sqrt{2} F\left (\sin ^{-1}\left (\frac{\sqrt{x+1}}{\sqrt{3}}\right )|-\frac{3}{2}\right ) \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[2 - x]*Sqrt[1 + x]*Sqrt[3 + x]),x]
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Rubi in Sympy [A] time = 3.98597, size = 24, normalized size = 1. \[ \sqrt{2} F\left (\operatorname{asin}{\left (\frac{\sqrt{3} \sqrt{x + 1}}{3} \right )}\middle | - \frac{3}{2}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(2-x)**(1/2)/(1+x)**(1/2)/(3+x)**(1/2),x)
[Out]
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Mathematica [B] time = 0.112191, size = 67, normalized size = 2.79 \[ -\frac{2 (x+3) \sqrt{1-\frac{5}{x+3}} \sqrt{1-\frac{2}{x+3}} F\left (\sin ^{-1}\left (\frac{\sqrt{5}}{\sqrt{x+3}}\right )|\frac{2}{5}\right )}{\sqrt{-5 (x+3)^2+35 (x+3)-50}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[2 - x]*Sqrt[1 + x]*Sqrt[3 + x]),x]
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Maple [B] time = 0.099, size = 44, normalized size = 1.8 \[ -{\frac{\sqrt{3}}{3+3\,x}{\it EllipticF} \left ({\frac{1}{2}\sqrt{-2-2\,x}},{\frac{i}{3}}\sqrt{3}\sqrt{2} \right ) \sqrt{-2-2\,x}\sqrt{2+2\,x}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(2-x)^(1/2)/(1+x)^(1/2)/(3+x)^(1/2),x)
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Maxima [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x + 3} \sqrt{x + 1} \sqrt{-x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 3)*sqrt(x + 1)*sqrt(-x + 2)),x, algorithm="maxima")
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Fricas [F] time = 0., size = 0, normalized size = 0. \[{\rm integral}\left (\frac{1}{\sqrt{x + 3} \sqrt{x + 1} \sqrt{-x + 2}}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 3)*sqrt(x + 1)*sqrt(-x + 2)),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- x + 2} \sqrt{x + 1} \sqrt{x + 3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(2-x)**(1/2)/(1+x)**(1/2)/(3+x)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{x + 3} \sqrt{x + 1} \sqrt{-x + 2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(x + 3)*sqrt(x + 1)*sqrt(-x + 2)),x, algorithm="giac")
[Out]